Question: Solve for $x$ and $y$ using elimination. ${3x+4y = 11}$ ${-3x-5y = -13}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {3x+4y = 11}\thinspace$ to find $x$ ${3x + 4}{(2)}{= 11}$ $3x+8 = 11$ $3x+8{-8} = 11{-8}$ $3x = 3$ $\dfrac{3x}{{3}} = \dfrac{3}{{3}}$ ${x = 1}$ You can also plug ${y = 2}$ into $\thinspace {-3x-5y = -13}\thinspace$ and get the same answer for $x$ : ${-3x - 5}{(2)}{= -13}$ ${x = 1}$